#include <stdio.h>
#include <stdlib.h>
#include <gmp.h>
#include <time.h>
#include <sys/time.h>
#include <vector>

bool factor(const mpz_t n);
void pollard_brent(mpz_t res, const mpz_t n, int c_int);
void pollard(mpz_t res, const mpz_t n, int c_int);
void f(mpz_t res, const mpz_t x, const mpz_t n, const mpz_t c);
int trialDivision(const mpz_t n);

//static int constants[] = {3,2,1,4,5,6,7,8,9};
static int constants[] = {1,2,3,4,5,6,7,8,9};
static int constants_size = 9;

double total_time_limit = 14.70;
double pollard_time_limit = 0.25;
double pollard__per_constant_time_limit = 0.13;
double start_time_pollard;
double start_time_pollard_per_constant;

//pollard variables

//mpz_t f1;
//mpz_t f2;

mpz_t y;
mpz_t c;
mpz_t m;

mpz_t g;
mpz_t r;
mpz_t q;

mpz_t x;
mpz_t ys;

mpz_t i;
mpz_t k;
mpz_t rkdif;
mpz_t xydif;

std::vector<char*> factors;

struct timeval real_time;

int main()
{
	mpz_t j;
	mpz_init (j);

	//init pollard variables
	
	//mpz_init (f1);
	//mpz_init (f2);
	
	mpz_init(y);
	mpz_init(c); 
	mpz_init(m);
	
	mpz_init (g);
	mpz_init (r); 
	mpz_init (q);
	
	mpz_init(x);
	mpz_init(ys);
	
	mpz_init(i);
	mpz_init(k);
	mpz_init(rkdif);
	mpz_init(xydif);
	
    gettimeofday(&real_time, NULL);
    double start = real_time.tv_sec + ((double)real_time.tv_usec)/1000000.0;
	
	while(0 != mpz_inp_str (j, stdin, 10))
	{
		factors.clear();
		
		gettimeofday(&real_time, NULL);
		start_time_pollard = real_time.tv_sec + ((double)real_time.tv_usec)/1000000.0;
		if(start_time_pollard - start > total_time_limit)
		{
			printf("fail\n");
			printf("\n");
		}
		else
		{
			if(!factor(j))
			{
				printf("fail\n");
			}
			else
			{
				for(int print_i=0;print_i< factors.size();print_i++)
				{
					printf("%s\n", factors[print_i]);
				}
			}
			printf("\n");
		}
	}
	
	return 0;
}
// 0 == fail
// 1 == OK
bool factor(const mpz_t n)
{
	mpz_t f1;
	mpz_t f2;
	mpz_init (f1);
	mpz_init (f2);

	
	int res = trialDivision(n);
	if(res != -1 && mpz_cmp_si(n, res) != 0){
		char* str = (char*)malloc(10);
		sprintf(str,"%d",res);
		factors.push_back(str);

		mpz_divexact_ui (f2, n, res);
		if(!factor(f2))
		{
			mpz_clear(f1);
			mpz_clear(f2);
			return 0; // fail
		}
	}
	else if(mpz_probab_prime_p (n, 5) > 0){
		factors.push_back(mpz_get_str (NULL, 10, n));
	}
	else{
		if( 0 != mpz_perfect_square_p(n) && 0 != mpz_root(f1, n, 2))
		{
		}
		else
		{
			for(int i=0;i< constants_size;i++)
			{
				gettimeofday(&real_time, NULL);
				start_time_pollard_per_constant = real_time.tv_sec + ((double)real_time.tv_usec)/1000000.0;
				//pollard_brent(f1, n, i);
				pollard_brent(f1, n, constants[i]);
				//pollard(f1, n, constants[i]);
				if(mpz_cmp_si(f1, 1) != 0)
				{
					break;
				}
			}
		}
		
		if(mpz_cmp_si(f1, 1) == 0)
		{
			//fail
			mpz_clear(f1);
			mpz_clear(f2);
			return 0; // fail
		}
		else
		{
			mpz_divexact (f2, n, f1);
			if(!factor(f1) || !factor(f2))
			{
				mpz_clear(f1);
				mpz_clear(f2);
				return 0; // fail
			}
		}
	}
	mpz_clear(f1);
	mpz_clear(f2);
	return 1; // OK
}

void pollard_brent(mpz_t res, const mpz_t n, int c_int)
{
	mpz_set_si(y, 0);
	//mpz_set_si(c, 2); // Set to constant 
	mpz_set_si(c, c_int);
	mpz_set_si(m, 1);

	mpz_set_si(g, 1);
	mpz_set_si(r, 1);
	mpz_set_si(q, 1);
	
	mpz_set(x, y);
	mpz_set(ys, y);
	
	struct timeval real_time;
	
	while(mpz_cmp_si(g, 1) == 0){
		
		//TODO Time check!
		gettimeofday(&real_time, NULL);
		double time = real_time.tv_sec + ((double)real_time.tv_usec)/1000000.0;
		if(time - start_time_pollard > pollard_time_limit)
		{
			mpz_set_si(res, 1);
			return;
		}
		else if(time - start_time_pollard_per_constant > pollard__per_constant_time_limit)
		{
			mpz_set_si(res, 1);
			return;
		}
		
		mpz_set(x, y);
		mpz_set_si(i, 0);
		while(mpz_cmp(i, r) < 0){
			f(y, y, n, c);
			mpz_add_ui(i, i, 1);
		}
		
		mpz_set_si(k, 0);
		while(mpz_cmp(k, r) < 0 && mpz_cmp_si(g, 1) == 0){
			//TODO Time check!
			mpz_set(ys, y);
			mpz_set_ui(i, 0);
			mpz_sub (rkdif, r, k);
			while(mpz_cmp(i, rkdif) < 0){
				
				f(y, y, n, c);
				mpz_sub(xydif, x, y);
				mpz_abs(xydif, xydif);
				mpz_mul(q, q, xydif);
				mpz_mod(q, q, n);
				mpz_add_ui(i, i, 1);
				mpz_sub (rkdif, r, k);
			}
			mpz_gcd(g, q, n);
			mpz_add (k, k, m);
		}
		mpz_mul_si(r, r, 2);
	}
	if(mpz_cmp(g, n) != 0){
		mpz_set(res, g);
	}
	else{
		mpz_set_si(res, 1);
	}
}

void pollard(mpz_t res, const mpz_t n, int c_int)
{
	mpz_set_si(x, 2);
	mpz_set_si(y, 2);
	mpz_set_si(g, 1);
	mpz_set_si(c, c_int);
	
	while(mpz_cmp_si(g, 1) == 0)
	{
		gettimeofday(&real_time, NULL);
		double time = real_time.tv_sec + ((double)real_time.tv_usec)/1000000.0;
		if(time - start_time_pollard > pollard_time_limit)
		{
			mpz_set_si(res, 1);
			return;
		}
		else if(time - start_time_pollard_per_constant > pollard__per_constant_time_limit)
		{
			mpz_set_si(res, 1);
			return;
		}
		f(x, x, n, c);
		f(y, y, n, c);
		f(y, y, n, c);
		mpz_sub(xydif, x, y);
		mpz_abs(xydif, xydif);
		mpz_gcd(g, xydif, n);
	}
	if(mpz_cmp(g, n) != 0)
	{
		mpz_set(res, g);
	}
	else
	{
		mpz_set_si(res, 1);
	}
}

void f(mpz_t res, const mpz_t x, const mpz_t n, const mpz_t c)
{
	mpz_mul (res, x, x);
	mpz_add (res, res, c);
	mpz_mod (res, res, n);
}

int trialDivision(const mpz_t n)
{
	int primes[] = {
	2,3,5,7,11,13,17,19,23,29
	,31,37,41,43,47,53,59,61,67,71
	,73,79,83,89,97,101,103,107,109,113
	,127,131,137,139,149,151,157,163,167,173
	,179,181,191,193,197,199,211,223,227,229
	,233,239,241,251,257,263,269,271,277,281
	,283,293,307,311,313,317,331,337,347,349
	,353,359,367,373,379,383,389,397,401,409
	,419,421,431,433,439,443,449,457,461,463
	,467,479,487,491,499,503,509,521,523,541
	,547,557,563,569,571,577,587,593,599,601
	,607,613,617,619,631,641,643,647,653,659
	,661,673,677,683,691,701,709,719,727,733
	,739,743,751,757,761,769,773,787,797,809
	,811,821,823,827,829,839,853,857,859,863
	,877,881,883,887,907,911,919,929,937,941
	,947,953,967,971,977,983,991,997,1009,1013
	,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069
	,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151
	,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223
	,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291
	,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373
	,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451
	,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511
	,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583
	,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657
	,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733
	,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811
	,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889
	,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987
	,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053
	,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129
	,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213
	,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287
	,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357
	,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423
	,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531
	,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617
	,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687
	,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741
	,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819
	,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903
	,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999
	,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079
	,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181
	,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257
	,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331
	,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413
	,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511
	,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571
	,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643
	,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727
	,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821
	,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907
	,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989
	,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057
	,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139
	,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231
	,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297
	,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409
	,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493
	,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583
	,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657
	,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751
	,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831
	,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937
	,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003
	,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087
	,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179
	,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279
	,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387
	,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443
	,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521
	,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639
	,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693
	,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791
	,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857
	,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939
	,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053
	,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133
	,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221
	,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301
	,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367
	,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473
	,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571
	,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673
	,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761
	,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833
	,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917
	,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997
	,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103
	,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207
	,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297
	,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411
	,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499
	,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561
	,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643
	,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723
	,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829
	,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919
	};
	
	for(int i = 0; i < 1000; i++){
		if(mpz_divisible_ui_p(n, primes[i]) != 0)
		{ 
			return primes[i];
		}
	}
	return -1;
}